Super-roughening as a disorder-dominated flat phase

¹ Grupo Interdisciplinar de Sistemas Complejos (GISC) () and Departamento de Matemáticas, Universidad Carlos III de Madrid Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
² Theoretical Division and Center for Nonlinear Studies, MS B258 Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Received: 5 January 2004
Accepted: 25 March 2004

Abstract

We study the phenomenon of super-roughening found on surfaces growing on disordered substrates. We consider a one-dimensional version of the problem for which the pure, ordered model exhibits a roughening phase transition. Extensive numerical simulations combined with analytical approximations indicate that super-roughening is a regime of asymptotically flat surfaces with non-trivial, rough short-scale features arising from the competition between surface tension and disorder. Based on this evidence and on previous simulations of the two-dimensional random sine-Gordon model (Sánchez et al. , Phys. Rev. E 62 (2000) 3219), we argue that this scenario is general and explains equally well the hitherto poorly understood two-dimensional case.